On Pillai's Problem involving Lucas sequences of the second kind
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866912411878948864 |
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| author | Heintze, Sebastian Ziegler, Volker |
| author_facet | Heintze, Sebastian Ziegler, Volker |
| contents | In this paper we consider the Diophantine equation $ V_n - b^m = c $ for given integers $ b,c $ with $ b \geq 2 $, whereas $ V_n $ varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation has at least three solutions $ (n,m) $, then there is an upper bound on the size of the solutions as well as on the size of the coefficients in the characteristic polynomial of $ V_n $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_11173 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Pillai's Problem involving Lucas sequences of the second kind Heintze, Sebastian Ziegler, Volker Number Theory In this paper we consider the Diophantine equation $ V_n - b^m = c $ for given integers $ b,c $ with $ b \geq 2 $, whereas $ V_n $ varies among Lucas-Lehmer sequences of the second kind. We prove under some technical conditions that if the considered equation has at least three solutions $ (n,m) $, then there is an upper bound on the size of the solutions as well as on the size of the coefficients in the characteristic polynomial of $ V_n $. |
| title | On Pillai's Problem involving Lucas sequences of the second kind |
| topic | Number Theory |
| url | https://arxiv.org/abs/2309.11173 |